A090770 a(n) = 2^(n^2 + 2n + 1)*Product_{j=1..n} (4^j - 1).

2, 48, 23040, 185794560, 24257337753600, 50821645356918374400, 1704875112338069448032256000, 915241991059360703024740763172864000, 7861748876453505095791592854589753555681280000, 1080506416218846625176535970968094253434513802154475520000, 2376056471052200653607636735377527394627947719754523173734842368000000

Offset: 0

Author

N. J. A. Sloane, Feb 10 2004

Keywords

• nonn

Comments

The order of the p-Clifford group for an odd prime p is a*p^(n^2+2n+1)*Product_{j=1..n} (p^(2*j)-1), where a = gcd(p+1,4). This is the sequence obtained by (illegally) setting p = 2.

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Crossrefs

Cf. A001309, A003956, A100221.

Cf. A092299 and A092301 (p=3), A092300 and A089989 (p=5), A090768 and A090769 (p=7).

A bisection of A003053, cf. A003923.

Programs

Mathematica

Table[2^(n^2+2n+1) Product[4^j-1,{j,n}],{n,0,10}] (* Harvey P. Dale, May 14 2022 *)

Python

from math import prod
def A090770(n): return prod((1<Chai Wah Wu, Jun 20 2022

Formula

a(n) ~ c * 2^((n+1)*(2*n+1)), where c = A100221. - Amiram Eldar, Jul 06 2025